Take the Deep Learning — Lecture 2, Set 04: 20 multiple-choice questions (30 minutes) with instant scoring and a full answer review. Covers 20 Deep…
The first 5 questions of this test, with the correct answer and explanation.
Q1. In the printed training output, what are the loss and accuracy after Epoch 1 of 5?
- A. loss 0.1035 and accuracy 0.9692
- B. loss 0.2524 and accuracy 0.9273 ✓
- C. loss 0.0000 and accuracy 1.0000
- D. loss 2.3026 and accuracy 0.1000
Answer: B. loss 0.2524 and accuracy 0.9273
Explanation: Epoch 1/5 prints loss: 0.2524 and acc: 0.9273; by Epoch 2 the loss has fallen to 0.1035 with acc 0.9692.
Q2. Before any preprocessing, what does train_labels contain?
- A. One-hot vectors of length 10
- B. Floating-point values between 0 and 1
- C. An array of digit values such as [5, 0, 4, ...] with dtype uint8 ✓
- D. Strings naming each digit
Answer: C. An array of digit values such as [5, 0, 4, ...] with dtype uint8
Explanation: train_labels is an array of digit values, array([5, 0, 4, ..., 5, 6, 8], dtype=uint8), with 60000 entries.
Q3. The naive_relu function loops over every entry and sets x[i, j] = max(x[i, j], 0). What is the optimised NumPy equivalent?
- A. z = np.dot(x, 0)
- B. z = x.reshape(-1)
- C. z = np.sum(x, axis=0)
- D. z = np.maximum(x, 0) ✓
Answer: D. z = np.maximum(x, 0)
Explanation: NumPy runs the same loops in optimised C: z = np.maximum(x, 0) for relu, and z = x + y for addition.
Q4. Which of these is NOT an element-wise operation?
- A. relu applied to an activation tensor
- B. The dot product between a batch and a weight matrix ✓
- C. sigmoid applied to an activation tensor
- D. The addition of two activation tensors
Answer: B. The dot product between a batch and a weight matrix
Explanation: relu, sigmoid, tanh and the addition of two activations are all element-wise; the dot product combines entries across axes and is not.
Q5. If x has shape (300, 20), what is the shape of x.T, and what does transposition do?
- A. (20, 300), swapping axes so that x.T[i, j] = x[j, i] ✓
- B. (300, 20), leaving the shape unchanged but reversing the rows
- C. (6000,), flattening the tensor
- D. (300, 300), making the matrix square
Answer: A. (20, 300), swapping axes so that x.T[i, j] = x[j, i]
Explanation: Transposition swaps axes: x of shape (300, 20) becomes (20, 300), with x.T[i, j] = x[j, i].
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Q6. Why does the lecture say transposition matters?
- A. It halves the memory needed for a weight matrix
- B. It converts a tensor to a lower precision data type
- C. It is what makes the shape rule of the dot product line up
- D. It is required before every element-wise operation
Q7. Plain vector data is stored as which kind of tensor?
- A. 1D tensors of shape (features,)
- B. 2D tensors of shape (samples, features)
- C. 3D tensors of shape (samples, time-steps, features)
- D. 4D tensors of shape (samples, height, width, channels)
Q8. Video data is stored as which kind of tensor?
- A. 3D tensors of shape (samples, frames, features)
- B. 4D tensors of shape (samples, frames, height, width)
- C. 5D tensors of shape (samples, frames, height, width, channels)
- D. 6D tensors of shape (samples, frames, height, width, channels, time)
Q9. In the geometric view, what is a 784-pixel MNIST image?
- A. A point in 784-dimensional space
- B. A line in 28-dimensional space
- C. A plane in 10-dimensional space
- D. A scalar value between 0 and 1
Q10. What does multiplying by W do to space, in the geometric view?
- A. It folds the negative half of every axis onto zero
- B. It translates every point by the same amount
- C. It rotates, scales and shears space, but keeps straight lines straight and the origin fixed
- D. It projects every point onto a single axis
Q11. What does training search for, in the geometric description of a deep network?
- A. The shortest chain of transformations that preserves the input exactly
- B. The chain of transformations that untangles the classes, so a final flat boundary separates the digits
- C. The transformation that maps every image to the origin
- D. The rotation that aligns the data with the coordinate axes
Q12. What is the formula for the sigmoid function, and what is its output range?
- A. max(0, x), with range [0, infinity)
- B. 1 / (1 + e to the minus x), with range (0, 1)
- C. (e^x - e^-x) / (e^x + e^-x), with range (-1, 1)
- D. e^z_i divided by the sum of e^z_j, with range (0, 1) summing to 1
Q13. What is the output range of tanh, and where is it typically used?
- A. (0, 1); output layer for binary classification
- B. [0, infinity); default for hidden layers
- C. (-1, 1); hidden layers in recurrent nets, because it is zero-centred
- D. (0, 1) summing to 1; output layer for K classes
Q14. What is the derivative of the sigmoid function?
- A. sigma(x) times (1 - sigma(x))
- B. 1 - tanh squared of x
- C. 1 if x > 0, else 0
- D. sigma(x) times x
Q15. What does it mean that sigmoid and tanh saturate, and what problem does it cause?
- A. Their output grows without bound, causing numerical overflow
- B. Their derivative becomes exactly 1, causing exploding gradients
- C. They produce only negative values, blocking the forward pass
- D. For |x| greater than about 4 their derivative is close to 0, so the gradient reaching earlier layers shrinks at every layer
Q16. What is a dead ReLU unit, and what variant is suggested to avoid it?
- A. A unit whose weights have grown too large; softmax is used instead
- B. A unit with x < 0 for all inputs, which has zero gradient and never recovers; Leaky ReLU, max(0.01x, x), keeps a small slope
- C. A unit that outputs the same value for every input; batch normalisation fixes it
- D. A unit removed by dropout; increasing the dropout rate avoids it
Q17. Why is softmax applied to the whole vector of scores rather than entry by entry?
- A. Because it would otherwise return negative values
- B. Because the scores must be sorted first
- C. Because raising one score lowers every other probability, which is what a K-way choice requires
- D. Because entry-by-entry application would be too slow
Q18. How does the lecture relate sigmoid to softmax?
- A. Sigmoid is softmax with K = 2: with scores (z, 0), the first output equals sigma(z)
- B. Softmax is sigmoid applied twice in sequence
- C. They are unrelated functions used in different eras
- D. Sigmoid is softmax with the exponential replaced by a logarithm
Q19. With three scores one unit apart, what ratio does softmax produce between the probabilities, and what about a gap of 5?
- A. A ratio of 2 for a gap of 1, and 10 for a gap of 5
- B. A ratio of e, about 2.7, for a gap of 1, and about 150 for a gap of 5
- C. A ratio of 1 for any gap, since softmax is shift-invariant
- D. A ratio of 5 for a gap of 1, and 25 for a gap of 5
Q20. How do libraries avoid overflow when computing softmax, and why is it valid?
- A. They clip all scores to the range (-10, 10), which changes the result only slightly
- B. They use float64 instead of float32, which removes the overflow
- C. They compute softmax(z - max z), which is the same function by the shift property
- D. They normalise the scores to sum to 1 before exponentiating